Cycles in Enhanced Hypercube Networks

Topology selection plays a key important role in the design of computer networks because it decides many crucial features and consequently has overwhelming impact on the network´s performance. Among the choices of network topologies the hypercube Q_n is popular because of its nice properties. Recently a more efficient network called enhanced hypercube network (denoted by Q_n,k) has been proposed to enhance the performance and reliability of hypercube. However, despite a lot of advantages discovered, many important properties of enhanced hypercube networks still remains unknown, which prevents the further applications of enhanced hypercube networks in critical areas. This paper aims to discover some important unknown features of enhanced hypercube networks through the topology property analysis. For this purpose, the structural natures of Q_n,k are investigated in detail. The properties related to cycles embedding into Q_n,k have been investigated. It is obtained that Q_n,k is bipartite if and only if n and k have same parity. We also obtained that if n and k have same parity, then every edge of Q_n,k lies on a cycle of every even length from 4 to 2ⁿ, and if n and k have different parity, then every edge of Q_n,k lies on a cycle of every even length from 4 to 2ⁿ and every odd length of n-k+2 to 2ⁿ-1.